The purpose of this project is to study whether techniques of treatment that preserve the breast (lumpectomy followed by radiation therapy) provide equal survival opportunity when compared to women treated with standard surgical techniques (mastectomy) for primary breast cancer. After a workup confirms localized disease, the patients are randomized to treatment with either mastectomy or lumpectomy plus radiation therapy. Both groups have axillary node dissections and are treated with chemotherapy should the nodes be positive.